Testing seasonal adjustment with Demetra

1
Testing seasonal adjustment with Demetra

• Dovnar Olga AlexandrovnaThe National Statistical
  Committee, Republic of Belarus

2
Check the original time series

• This report presents the results of the seasonal
  adjustment of time series of the index of
  industrial production of the Republic of Belarus
• Conclusions about the quality of source data
• Original time series is a monthly index of
  industrial production with base year 2005
• Length of time series is 72 observations
  (1.2005-12.2010)
• In 2011, the statistical classification NACE/ISIC
  rev.3 was introduced into the practice of the
  Republic of Belarus. In this regard, this time
  series of indices of industrial production by
  NACE was obtained not by processing raw data, but
  by recalculating the structure of previously
  existing series of monthly indices based on the
  previous classification.
• The quality of the series received in that way
  Belstat considers not sufficiently precise, but
  quite satisfactory for statistical analysis, as
  the proportion of data relating to the industry
  by NCES is 98 of the total industrial output by
  NACE.
• In process of receipt of the new observations
  based on NACE, the quality of the time series
  will be improved.

3
The presence of seasonality in the original
series

• Fig. 1
• In the original time series a seasonal factor is
  present, what is indicated by the presence of
  spectral peaks at seasonal frequencies, and
  calendar effects.

4
Approach and predictors

• The approach TRAMO/SEATS was used
• User-defined specification TramoSeatsSpec-1 was
  used

Options Values
Transformation Function Auto
Calendar holidays of Belarus, td2
The Easter No
Automatic modelling ARIMA True
Deviating values True
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Pre-treatment

• The estimated period 1-2005 12-2010
• Logarithmically transformed series was chosen.
• Calendar effects (2 variables the working days,
  a leap year). No effects of Easter.
• Type of used model is ARIMA model
  (0,1,1)(0,1,1)..
• Deviating values ??identified one deviating
  value in November.

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Graph of results

• Fig. 2
• Seasonal component in the irregular component is
  not lost

7
Decomposition

• The basic model ARIMA of the time series of
  industrial production indices of the Republic of
  Belarus (1-0,34?)(1 - 0,25 B12)at , s2 1,
• decomposed into three sub-models
• Trend model (1 0,1B - 0,9B2)ap,t., s2
  0,0334
• Seasonal model (1 1,43B 1,51B2 1,45 B3
  1,25B4 1,01B5 0,74B6 0,47B7 0,24B8
  0,03B9 0,11B10 - 0,40B11)as,t, s2 0,1476
• Irregular model white noise (0 0,1954).
• Dispersion of seasonal and trend components are
  lower than the irregular component. This means
  that stable trend and seasonal components were
  obtained.

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The main diagnostic of quality
Diagnosis and result Explanation
Summary Good In general, good quality seasonal adjustment means that an adequate model of decomposition is chosen
basic checks definition Good (0,000) annual totals Good (0,003) Match the annual totals of the original series and the seasonally adjusted series.
visual spectral analysis spectral seas peaks Good spectral td peaks Good In the original series seasonal peaks and peaks of days are visually present
Friedman statistic 8,7207, P-value0.000. Kruskall-Wallis st. 47,1172, P-value0.000 In the original series are present stable seasonal variations in the level of significance of 1.
regarima residuals normality Good (0,461 ) independence Good (0,873 ) spectral td peaks Uncertain (0,088) spectral seas peaks Uncertain (0,024) Residuals distributed normally, randomly and independently. The uncertainty of the visual assessment of spectral seasonal peaks and peaks of operating days in residuals (perhaps there are seasonal and calendar effects in residuals)
residual seasonality on sa Good (0,978) on sa (last 3 years) Good (0,994) on irregular Good (1,000) There are no seasonal effects in the seasonally adjusted series, during the last 3 years, as well in the irregular components series.
Residual seasonality testNo evidence of residual seasonality in the entire series at the 10 per cent level F0,3231No evidence of residual seasonality in the last 3 years at the 10 per cent level F0,2228 There are no indications of residual seasonal fluctuations in the entire series at 10 significance level.
outliers number of outliers Good (0,014) There are diverging values, but their number is not critical
seats seas variance Good (0,374) irregular variance Good (0,323) seas/irr cross-correlation Good (0, 113) Trend, seasonal and irregular component are independent (uncorrelated).

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Check on a sliding seasonal factor
Fig. 3
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Stability of the model
Seasonally adjusted series (SA) Trend
Fig. 4 Fig. 5 Mean0,3792 rmse0.6888

Mean0,3792
rmse0.6888
January -0.009 July 0.380
February 1.211 August 0.831
March 1.259 September 0.509
April -0.249 October -0.363
May 0.113 November -0.385
June 0.794 December
January 0.222 July 0.369
February 1.167 August 1.128
March 1.976 September 1.138
April -0.196 October -0.517
May -0.077 November -0.697
June 1.042 December

• The graphs of seasonally adjusted series (SA,
  Fig. 4) and trend (Fig. 5) shows that the updates
  are insignificant. The model can be considered as
  stable, because the difference between the first
  and the last estimates does not exceed 3. There
  is one value on the graph of the Trend, exceeding
  the critical limit (March 2010 1.976).

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Analysis of the residuals

• Fig. 6
• The test results shows that residuals are
  independent, random and normal. Tests for
  nonlinearity did not show non-linearity in the
  form of trends.

P-value
Ljung-Box on squared residuals(24) 0,8708
Box-Pierce on squared residuals(24) 0,9670
12
Residual seasonal factor

• Fig. 7
• We can assume that there are no indicators of
  residual seasonal fluctuations in the residues.
  But there is one peak at the small spectral
  seasonal frequency and one at the frequency of
  operating days, which may mean that the used
  filters are not the best to remove them.

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Some problematic results

• How to connect the national calendar of holidays
  when applying built-in specs?
• The curve of the seasonality graph has not a
  visually clear structure (Fig. 8). How to
  interpret this?
• When using the model ARIMA model (0, 1, 0)(1, 0,
  0) a purple line appeared on the chart (Fig. 9).
  What does it mean?
• What does the lack of graphs in the
  autoregressive spectrum of the spectral analysis
  of residuals mean? Is it a problem if there are
  small spectral peaks in the periodogram? (Fig. 7,
  slide 12).

Fig. 9
Fig. 8
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Some problematic results (continued)

• 5. How to correctly interpret a situation where
  innovation variance of the irregular component is
  lower than the trend and seasonality when using
  the ARIMA (0,1,0)(1, 0, 0) model?
• trend. Innovation variance 0,0821
• seasonal. Innovation variance 0,1989
• irregular. Innovation variance 0,0971

6. Is it a problem if there is hypothetical
autocorrelation in the seasonally adjusted series
of lag 6, with using the ARIMA (0,1,1)(0, 1, 1)
model? Autocorrelation function seasonal
Lag Component Estimator Estimate PValue
6 0,1167 -0,6202 -0,2898 0,0490
7. Can they be considered as acceptable results
of the Ljung-Box and Box-Pierce tests for the
presence of seasonality in residuals at lags 24
and 36 when using ARIMA (0,1,0) (1, 0, 0), or
does it mean not using a suitable model?
Lag Autocorrelation Standard deviation Ljung-Box test P-Value
24 0,1918 0,1187 4,9482 0,0261
36 -0,1103 0,1187 6,7510 0,0342